On the distribution of functionals of Brownian local time

The definition of Brownian local time is given and its properties are considered. An important aspect is the approximation of Brownian motion and its local time by means of random walks. A special interest in the study of the Brownian local time is the description of the local time as a Markov process with respect to the space parameter. This description is used to deduce the result on the distribution of integral functionals and functionals of supremum type of Brownian local time.